Force and Work Fluctuations for Langevin Dynamics in Time-dependent Potential

Work processes over small particles in a viscous white-noise environment (thermal bath) are governed by a set of theorems of stochastic thermodynamics such as, e.g., Jarzynski relation and Crooks fluctuation theorem. These theoretical results assume Langevin kinetics of particles in an equilibrium heat bath whose properties are not affected by external driving. The wide applicability of conclusions provided by stochastic thermodynamics reflects the fact that many of them are not perturbative with respect to driving force magnitude and are valid for any observation period. Based on fluctuation theorems and solutions of the overdamped Langevin equation and the Fokker–Planck equation in linear models, we investigate statistics of external force and work in process of particle transport in moving confining potential. Analysis reveal conditions under which the work fluctuations are relatively small compared to the mean value so that the noise affected transport process can be treated as well controllable. In addition, a relationship between the mean squared fluctuation of the force applied to a particle by time-dependent potential and the correlation time of the force is derived indicating that product of these two quantities does not depend on details of the work protocol.